SUMMARY Much mental health research uses neurophysiological measurements to describe the way neural activity within and across brain regions is related to behavioral function and dysfunction. One kind of signal, known as a spike train, comes from an individual neuron. Another, the local field potential (LFP), is based on activity from large numbers of neurons within specified parts of the brain. For both kinds of data, scientifically rigorous statistical analysis must accommodate unstable fluctuations, associated with movement or thought, known in statistics as non-stationarity. The continuing research program of this grant is to develop methods for analyzing non-stationary neural data. The number of neural signals that can be recorded simultaneously has been increasing rapidly. Because neural network dysfunction is widely considered to be associated with psychopathology, improvements in recording technologies offer exciting opportunities, but they also create big statistical challenges due to greatly increased complexity. To provide the most useful information for designing novel therapies it is important to characterize the interactions among different parts of the brain, and the timing of these interactions relative to behavior. The research in this grant aims to develop methods for analyzing the ways that a network of brain areas may change with particular variables, including those that help characterize behavior. This involves the transmission of neural information at multiple timescales: slower timescales can provide insight into states of the brain, such as the extent to which a subject is paying attention to a task; fast timescales include oscillations and neural synchrony, which could provide an essential mechanism of neural network information flow and may be a marker that distinguishes normal from diseased states. New methods investigated in this research program can accommodate both faster and slower timescales, and they can also accommodate relationships arising from the spatial configuration of electrodes that record neural signals. Because a neural spike train is a set of times at which a neuron fired, it is common to consider it to be a point process, which is the statistical model set up to handle sequences of event times. The research supported by this grant concerns development and investigation of statistical techniques involving both multi-dimensional continuous time series (for LFPs) and multi-dimensional point processes (for spike trains).